How do I configure Exim to send all non-local mail to a gateway host?

Replace the dnslookup router in the default configuration with the following:

send_to_gateway:
  driver = manualroute
  domains = !+local_domains
  transport = remote_smtp
  route_list = * gate.way.host

If there are several hosts you can send to, you can specify them as a colon-separated list.